Question: Simplify the following expression: $\dfrac{18z^2}{90z^2}$ You can assume $z \neq 0$.
Explanation: $ \dfrac{18z^2}{90z^2} = \dfrac{18}{90} \cdot \dfrac{z^2}{z^2} $ To simplify $\frac{18}{90}$ , find the greatest common factor (GCD) of $18$ and $90$ $18 = 2 \cdot 3 \cdot 3$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $ \mbox{GCD}(18, 90) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{18}{90} \cdot \dfrac{z^2}{z^2} = \dfrac{18 \cdot 1}{18 \cdot 5} \cdot \dfrac{z^2}{z^2} $ $\phantom{ \dfrac{18}{90} \cdot \dfrac{2}{2}} = \dfrac{1}{5} \cdot \dfrac{z^2}{z^2} $ $ \dfrac{z^2}{z^2} = \dfrac{z \cdot z}{z \cdot z} = 1 $ $ \dfrac{1}{5} \cdot 1 = \dfrac{1}{5} $